Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites-axons and dendrites-to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Automated summary

The establishment of a functioning neuronal network involves the migration, growth, and morphogenesis of neurites, which rely on multiple biophysical effects and sensory cues. Mathematical models are useful for testing hypotheses and understanding the underlying mechanisms of neuron development. This review focuses on different mathematical models for neurite growth and morphogenesis, emphasizing mechanics and mechanisms and simple analytical treatment.